König's work on the factorisation of bipartite graphs relates closely to the marriage problem of Philip Hall.

Most coral reef fishes have a bipartite life cycle, with a dispersing pelagic larval phase and a relatively sedentary reef resident phase.

It becomes clear fairly quickly once you start playing with examples that the thing to do is create some kind of bipartite graph, where the left side is the ‘bad answer’ and the right side is the ‘good answer’.